---
id: 5900f3d61000cf542c50fee8
title: 'Problema 105: Somas especiais de subconjuntos: testes'
challengeType: 1
forumTopicId: 301729
dashedName: problem-105-special-subset-sums-testing
---

# --description--

Deixe que $S(A)$ represente a soma dos elementos no conjunto A, de tamanho n. Vamos chamá-la de uma soma especial definida se, para dois subconjuntos disjuntos, B e C, as seguintes propriedades são verdadeiras:

1. $S(B) ≠ S(C)$; isto é, as somas de subconjuntos não podem ser iguais.
2. Se B contém mais elementos que C, $S(B) > S(C)$.

Por exemplo, {81, 88, 75, 42, 87, 84, 86, 65} não é uma soma especial porque 65 + 87 + 88 = 75 + 81 + 84, enquanto {157, 150, 164, 119, 79, 159, 161, 139, 158} satisfaz as duas regras para todas as combinações possíveis de pares de subconjuntos e $S(A) = 1286$.

Usando `sets` (conjuntos), um array com cem conjuntos, contendo de sete a doze elementos (os dois exemplos citados acima são os dois primeiros conjuntos), identifique todos os conjuntos especiais de soma, $A_1, A_2, \ldots, A_k$, e encontre o valor de $(A_1) + S(A_2) + \cdots + S(A_k)$.

**Observação:** este problema está relacionado aos problemas 103 e 106.

# --hints--

`testingSpecialSubsetSums(testSets)` deve retornar `73702`.

```js
assert.strictEqual(testingSpecialSubsetSums(_testSets), 73702);
```

# --seed--

## --after-user-code--

```js
const _testSets = [
  [81,88,75,42,87,84,86,65],[157,150,164,119,79,159,161,139,158],[673,465,569,603,629,592,584,300,601,599,600],[90,85,83,84,65,87,76,46],[165,168,169,190,162,85,176,167,127],[224,275,278,249,277,279,289,295,139],[354,370,362,384,359,324,360,180,350,270],[599,595,557,298,448,596,577,667,597,588,602],[175,199,137,88,187,173,168,171,174],[93,187,196,144,185,178,186,202,182],[157,155,81,158,119,176,152,167,159],[184,165,159,166,163,167,174,124,83],[1211,1212,1287,605,1208,1189,1060,1216,1243,1200,908,1210],[339,299,153,305,282,304,313,306,302,228],[94,104,63,112,80,84,93,96],[41,88,82,85,61,74,83,81],[90,67,84,83,82,97,86,41],[299,303,151,301,291,302,307,377,333,280],[55,40,48,44,25,42,41],[1038,1188,1255,1184,594,890,1173,1151,1186,1203,1187,1195],[76,132,133,144,135,99,128,154],[77,46,108,81,85,84,93,83],[624,596,391,605,529,610,607,568,604,603,453],[83,167,166,189,163,174,160,165,133],[308,281,389,292,346,303,302,304,300,173],[593,1151,1187,1184,890,1040,1173,1186,1195,1255,1188,1203],[68,46,64,33,60,58,65],[65,43,88,87,86,99,93,90],[83,78,107,48,84,87,96,85],[1188,1173,1256,1038,1187,1151,890,1186,1184,1203,594,1195],[302,324,280,296,294,160,367,298,264,299],[521,760,682,687,646,664,342,698,692,686,672],[56,95,86,97,96,89,108,120],[344,356,262,343,340,382,337,175,361,330],[47,44,42,27,41,40,37],[139,155,161,158,118,166,154,156,78],[118,157,164,158,161,79,139,150,159],[299,292,371,150,300,301,281,303,306,262],[85,77,86,84,44,88,91,67],[88,85,84,44,65,91,76,86],[138,141,127,96,136,154,135,76],[292,308,302,346,300,324,304,305,238,166],[354,342,341,257,348,343,345,321,170,301],[84,178,168,167,131,170,193,166,162],[686,701,706,673,694,687,652,343,683,606,518],[295,293,301,367,296,279,297,263,323,159],[1038,1184,593,890,1188,1173,1187,1186,1195,1150,1203,1255],[343,364,388,402,191,383,382,385,288,374],[1187,1036,1183,591,1184,1175,888,1197,1182,1219,1115,1167],[151,291,307,303,345,238,299,323,301,302],[140,151,143,138,99,69,131,137],[29,44,42,59,41,36,40],[348,329,343,344,338,315,169,359,375,271],[48,39,34,37,50,40,41],[593,445,595,558,662,602,591,297,610,580,594],[686,651,681,342,541,687,691,707,604,675,699],[180,99,189,166,194,188,144,187,199],[321,349,335,343,377,176,265,356,344,332],[1151,1255,1195,1173,1184,1186,1188,1187,1203,593,1038,891],[90,88,100,83,62,113,80,89],[308,303,238,300,151,304,324,293,346,302],[59,38,50,41,42,35,40],[352,366,174,355,344,265,343,310,338,331],[91,89,93,90,117,85,60,106],[146,186,166,175,202,92,184,183,189],[82,67,96,44,80,79,88,76],[54,50,58,66,31,61,64],[343,266,344,172,308,336,364,350,359,333],[88,49,87,82,90,98,86,115],[20,47,49,51,54,48,40],[159,79,177,158,157,152,155,167,118],[1219,1183,1182,1115,1035,1186,591,1197,1167,887,1184,1175],[611,518,693,343,704,667,686,682,677,687,725],[607,599,634,305,677,604,603,580,452,605,591],[682,686,635,675,692,730,687,342,517,658,695],[662,296,573,598,592,584,553,593,595,443,591],[180,185,186,199,187,210,93,177,149],[197,136,179,185,156,182,180,178,99],[271,298,218,279,285,282,280,238,140],[1187,1151,890,593,1194,1188,1184,1173,1038,1186,1255,1203],[169,161,177,192,130,165,84,167,168],[50,42,43,41,66,39,36],[590,669,604,579,448,599,560,299,601,597,598],[174,191,206,179,184,142,177,180,90],[298,299,297,306,164,285,374,269,329,295],[181,172,162,138,170,195,86,169,168],[1184,1197,591,1182,1186,889,1167,1219,1183,1033,1115,1175],[644,695,691,679,667,687,340,681,770,686,517],[606,524,592,576,628,593,591,584,296,444,595],[94,127,154,138,135,74,136,141],[179,168,172,178,177,89,198,186,137],[302,299,291,300,298,149,260,305,280,370],[678,517,670,686,682,768,687,648,342,692,702],[302,290,304,376,333,303,306,298,279,153],[95,102,109,54,96,75,85,97],[150,154,146,78,152,151,162,173,119],[150,143,157,152,184,112,154,151,132],[36,41,54,40,25,44,42],[37,48,34,59,39,41,40],[681,603,638,611,584,303,454,607,606,605,596]
];
```

## --seed-contents--

```js
function testingSpecialSubsetSums(sets) {

  return true;
}

const testSets = [
  [81,88,75,42,87,84,86,65],[157,150,164,119,79,159,161,139,158],[673,465,569,603,629,592,584,300,601,599,600],[90,85,83,84,65,87,76,46],[165,168,169,190,162,85,176,167,127],[224,275,278,249,277,279,289,295,139],[354,370,362,384,359,324,360,180,350,270],[599,595,557,298,448,596,577,667,597,588,602],[175,199,137,88,187,173,168,171,174],[93,187,196,144,185,178,186,202,182],[157,155,81,158,119,176,152,167,159],[184,165,159,166,163,167,174,124,83],[1211,1212,1287,605,1208,1189,1060,1216,1243,1200,908,1210],[339,299,153,305,282,304,313,306,302,228],[94,104,63,112,80,84,93,96],[41,88,82,85,61,74,83,81],[90,67,84,83,82,97,86,41],[299,303,151,301,291,302,307,377,333,280],[55,40,48,44,25,42,41],[1038,1188,1255,1184,594,890,1173,1151,1186,1203,1187,1195],[76,132,133,144,135,99,128,154],[77,46,108,81,85,84,93,83],[624,596,391,605,529,610,607,568,604,603,453],[83,167,166,189,163,174,160,165,133],[308,281,389,292,346,303,302,304,300,173],[593,1151,1187,1184,890,1040,1173,1186,1195,1255,1188,1203],[68,46,64,33,60,58,65],[65,43,88,87,86,99,93,90],[83,78,107,48,84,87,96,85],[1188,1173,1256,1038,1187,1151,890,1186,1184,1203,594,1195],[302,324,280,296,294,160,367,298,264,299],[521,760,682,687,646,664,342,698,692,686,672],[56,95,86,97,96,89,108,120],[344,356,262,343,340,382,337,175,361,330],[47,44,42,27,41,40,37],[139,155,161,158,118,166,154,156,78],[118,157,164,158,161,79,139,150,159],[299,292,371,150,300,301,281,303,306,262],[85,77,86,84,44,88,91,67],[88,85,84,44,65,91,76,86],[138,141,127,96,136,154,135,76],[292,308,302,346,300,324,304,305,238,166],[354,342,341,257,348,343,345,321,170,301],[84,178,168,167,131,170,193,166,162],[686,701,706,673,694,687,652,343,683,606,518],[295,293,301,367,296,279,297,263,323,159],[1038,1184,593,890,1188,1173,1187,1186,1195,1150,1203,1255],[343,364,388,402,191,383,382,385,288,374],[1187,1036,1183,591,1184,1175,888,1197,1182,1219,1115,1167],[151,291,307,303,345,238,299,323,301,302],[140,151,143,138,99,69,131,137],[29,44,42,59,41,36,40],[348,329,343,344,338,315,169,359,375,271],[48,39,34,37,50,40,41],[593,445,595,558,662,602,591,297,610,580,594],[686,651,681,342,541,687,691,707,604,675,699],[180,99,189,166,194,188,144,187,199],[321,349,335,343,377,176,265,356,344,332],[1151,1255,1195,1173,1184,1186,1188,1187,1203,593,1038,891],[90,88,100,83,62,113,80,89],[308,303,238,300,151,304,324,293,346,302],[59,38,50,41,42,35,40],[352,366,174,355,344,265,343,310,338,331],[91,89,93,90,117,85,60,106],[146,186,166,175,202,92,184,183,189],[82,67,96,44,80,79,88,76],[54,50,58,66,31,61,64],[343,266,344,172,308,336,364,350,359,333],[88,49,87,82,90,98,86,115],[20,47,49,51,54,48,40],[159,79,177,158,157,152,155,167,118],[1219,1183,1182,1115,1035,1186,591,1197,1167,887,1184,1175],[611,518,693,343,704,667,686,682,677,687,725],[607,599,634,305,677,604,603,580,452,605,591],[682,686,635,675,692,730,687,342,517,658,695],[662,296,573,598,592,584,553,593,595,443,591],[180,185,186,199,187,210,93,177,149],[197,136,179,185,156,182,180,178,99],[271,298,218,279,285,282,280,238,140],[1187,1151,890,593,1194,1188,1184,1173,1038,1186,1255,1203],[169,161,177,192,130,165,84,167,168],[50,42,43,41,66,39,36],[590,669,604,579,448,599,560,299,601,597,598],[174,191,206,179,184,142,177,180,90],[298,299,297,306,164,285,374,269,329,295],[181,172,162,138,170,195,86,169,168],[1184,1197,591,1182,1186,889,1167,1219,1183,1033,1115,1175],[644,695,691,679,667,687,340,681,770,686,517],[606,524,592,576,628,593,591,584,296,444,595],[94,127,154,138,135,74,136,141],[179,168,172,178,177,89,198,186,137],[302,299,291,300,298,149,260,305,280,370],[678,517,670,686,682,768,687,648,342,692,702],[302,290,304,376,333,303,306,298,279,153],[95,102,109,54,96,75,85,97],[150,154,146,78,152,151,162,173,119],[150,143,157,152,184,112,154,151,132],[36,41,54,40,25,44,42],[37,48,34,59,39,41,40],[681,603,638,611,584,303,454,607,606,605,596]
];

testingSpecialSubsetSums(testSets);
```

# --solutions--

```js
// solution required
```
